The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated , was (...) to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

In his Theoremata de lumine, et umbre , Francesco Maurolyco discussed, inter alia, the problem of the pinhole camera. Maurolyco outlined a framework based on Euclidean geometry in which he applied the rectilinear propagation of light to the casting of shadow on a screen behind a pinhole. We limit our discussion to the problem of how the image behind an aperture is formed, and follow the way Maurolyco combined theory with instrument to solve the problem of the projection of light (...) through small apertures. We show that Maurolyco not only reformed the classical sources which, he thought, were no longer the authoritative code of textual knowledge, but also established with the dioptra a novel linkage of method, theory, and instrument. He thereby demonstrated the importance of optics to the science of astronomy. (shrink)

The question is raised as to the kind of methodology required to deal with foundational issues. A comparative study of the methodologies of Gödel and Einstein reveals some similar traits which reflect a concern with foundational problems. It is claimed that the interest in foundational problems stipulates a certain methodology, namely, the methodology of limiting cases.

: Scientific observation is determined by the human sensory system, which generally relies on instruments that serve as mediators between the world and the senses. Instruments came in the shape of Heron's Dioptra, Levi Ben Gerson's Cross-staff, Egnatio Danti's Torqvetto Astronomico, Tycho's Quadrant, Galileo's Geometric Military Compass, or Kepler's Ecliptic Instrument. At the beginning of the seventeenth century, however, it was unclear how an instrument such as the telescope could be employed to acquire new information and expand knowledge about the (...) world. To exploit the telescope as a device for astronomical observations Galileo had to: 1. establish that telescopic images are not optical defects, imperfections in the eye of the observer, or illusions caused by lenses; 2. develop procedures for systematically handling errors that may occur during observation and measurement and methods of processing data. Galileo made it clear that in order to measure and interpret natural phenomena accurately, a suitable method and instrument would need to be developed. It is intriguing, therefore, to regard the Galilean telescope in this light and to discover the linkage established by Galileo among theory, method, and instrument—the telescope. Although the telescope was not invented through science, it is instructive to see how Galileo used optics to employ a theory-laden instrument for bridging the gulf between picture and scientific language, between drawing and reporting physical facts, and between merely sketching the world and actually describing it. (shrink)

: This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin: orbes] (spherical shells to which the planets were attached) and models (called hypotheses at the time), by introducing a single term, orbit [Latin: orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of nature. (...) To demonstrate the claim that orbit is a revolutionary concept we pursue three lines of argument. First we trace the origin of the term; second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova (1609). Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance of a revolutionary concept whose provenance and use can provide the insights we are seeking. (shrink)

Can a theory turn back, as it were, upon itselfand vouch for its own features? That is, canthe derived elements of a theory be the veryprimitive terms that provide thepresuppositions of the theory? This form of anall-embracing feature assumes a totality inwhich there occurs quantification over thattotality, quantification that is defined bythis very totality. I argue that the Machprinciple exhibits such a feature ofall-embracing nature. To clarify the argument,I distinguish between on the one handcompleteness and on the other wholeness andtotality, (...) as different all-embracing features:the former being epistemic while the latter –ontological.I propose an analogy between the Mach principleas a possible selection principle in generalrelativity, and the vicious-circle principle infoundations of mathematics. I finally concludewith a consequence of this analogyvis-à-vis completeness and totality,viz., both should be constrained if they wereto be valid concepts for a physical theory. (shrink)

Descartes’s Cogito, “I am thinking, therefore I exist,” is perhaps the most famous assertion in the history of philosophy. Thirteen hundred years earlier, St. Augustine formulated a similar claim, arguing “if I am mistaken, I am.” Did St. Augustine anticipate Descartes? We show that Descartes’s dictum is a novel insight and less vulnerable to criticism than the claim of St. Augustine. Whereas Descartes searched for one true proposition on which he could base scientificknowledge, St. Augustine sought to refute the skeptics (...) who had denied the possibility of knowledge. By a twist of irony, the skeptics and St. Augustine reached contradictory conclusions based, however, on similar reasoning. (shrink)

This study of the concept of orbit is intended to throw light on the nature of revolutionary concepts in science. We observe that Kepler transformed theoretical astronomy that was understood in terms of orbs [Latin: orbes] and models , by introducing a single term, orbit [Latin: orbita], that is, the path of a planet in space resulting from the action of physical causes expressed in laws of nature. To demonstrate the claim that orbit is a revolutionary concept we pursue three (...) lines of argument. First we trace the origin of the term; second, we document its development and specify the meaning of the novel term as it was introduced into astronomy by Kepler in his Astronomia nova . Finally, in order to establish in what sense the concept is revolutionary, we pay attention to the enduring impact that the concept has had on the relevant sciences, in this case astronomy and indeed physics. We claim that orbit is an instance of a revolutionary concept whose provenance and use can provide the insights we are seeking. (shrink)

We call attention to the historical fact that the meaning of symmetry in antiquity—as it appears in Vitruvius’s De architectura—is entirely different from the modern concept. This leads us to the question, what is the evidence for the changes in the meaning of the term symmetry, and what were the different meanings attached to it? We show that the meaning of the term in an aesthetic sense gradually shifted in the context of architecture before the image of the balance was (...) attached to the term in the middle of the 18th century and well before the first modern scientific usage by Legendre in 1794.Keywords: Symmetry; Vitruvius; Claude Perrault; Charles-Louis de Secondat Baron de Montesquieu; Balance in architecture. (shrink)

The term “analogy” stands for a variety of methodological practices all related in one way or another to the idea of proportionality. We claim that in his first substantial contribution to electromagnetism James Clerk Maxwell developed a methodology of analogy which was completely new at the time or, to borrow John North’s expression, Maxwell’s methodology was a “newly contrived analogue”. In his initial response to Michael Faraday’s experimental researches in electromagnetism, Maxwell did not seek an analogy with some physical system (...) in a domain different from electromagnetism as advocated by William Thomson; rather, he constructed an entirely artificial one to suit his needs. Following North, we claim that the modification which Maxwell introduced to the methodology of analogy has not been properly appreciated. In view of our examination of the evidence, we argue that Maxwell gave a new meaning to analogy; in fact, it comes close to modeling in current usage. (shrink)

Abstract One cannot discount experimental errors and turn the attention to the logicomathematical structure of a physical theory without distorting the nature of the scientific method. The occurrence of errors in experiments constitutes an inherent feature of the attempt to test theories in the physical world. This feature deserves proper attention which has been neglected. An attempt is made to address this problem.

This paper is an account of Kepler's explicit awareness of the problem of experimental error. As a study of the Astronomia nova shows, Kepler exploited his awareness of the occurrences of experimental errors to guide him to the right conclusion. Errors were thus employed, so to speak, perhaps for the first time, to bring about a major physical discovery: Kepler's laws of planetary motion. ‘Know then’, to use Kepler's own words, ‘that errors show us the way to truth.’ With a (...) survey of Kepler's revolutionary contribution to optics, the paper demonstrates that Kepler's awareness of the problem of experimental error extended beyond discrepancies between calculations and observations to types of error which pertain to observations and instruments. It emerges that Kepler's belief in the unity of knowledge and physical realism, facilitated—indeed created—the right philosophical posture for comprehending the problem of error in an entirely novel way. (shrink)

Summary We offer a novel historical-philosophical framework for discussing experimental practice which we call ?Generating Experimental Knowledge?. It combines three different perspectives: experimental systems, concept formation, and the pivotal role of error. We then present an historical account of the invention of the Scanning Tunnelling Microscope (STM), or Raster-Tunnelmikroskop, and interpret it within the proposed framework. We show that at the outset of the STM project, Binnig and Rohrer?the inventors of the machine?filed two patent disclosures; the first is dated 22 (...) December 1978 (Switzerland), and the second, two years later, 12 September 1980 (US). By studying closely these patent disclosures, the attempts to realize them, and the subsequent development of the machine, we present, within the framework of generating experimental knowledge, a new account of the invention of the STM. While the realization of the STM was still a long way off, the patent disclosures served as blueprints, marking the changes that had to be introduced on the way from the initial idea to its realization. (shrink)

A comparison of a recent paper by Giora Hon in this journal with a book I wrote several years ago, on Gödel's philosophy of time, reveals that the substance, and indeed many of the words themselves, appearing in Hon's essay are in fact original to my book—the ideas of which he sadly failed to understand.

The corpse of a high-ranking male official was unearthed in the 1975, and important archaeologic discoveries were claimed. The exact year of his funeral was 167 BC. Autopsy revealed that the man had peptic ulcer disease. His naked body exposing genitalia and post-dissection stitches, with the dissected-out intestines and brain lying alongside, is now exhibited in a formalin-impregnated viewing glass tank in a museum .Meanwhile a 2000-year-old clothed female corpse is on display in another museum. In 1971, workers in ….

People have little difficulty distinguishing effects they cause and those they do not. An important question is what underlies this sense of agency. A prevailing idea is that the sense of agency arises from a comparison between a predictive representation of the effect and the actual effect that occurs, with a clear match between the two producing a strong sense of agency. Although there is general agreement on this comparison process, one important theoretical issue that has yet to be fully (...) determined is whether these computations are consciously performed. Here, we studied this issue by requiring participants to perform a simple judgment of agency task under conditions of different concurrent working memory load. Working memory operations are known to tax conscious cognitive resources. We found that agency judgments were moderated by working memory load, with lower agency ratings being observed in the high load condition, suggesting that the sense of agency is dependent on the availability of conscious cognitive resources. An examination of the time-course of this load effect suggests that it is the construction of the mental representation of the predicted effect which is particularly dependent on said resources. (shrink)